After the two load steps (load then unload) you can run a third load step. Assuming you have large deflection on there is no need to export the deformed geometry. It is possible to do what you say, "use the deformed geometry and map the residual stress as initial stress" to another model, but it's not necesary if you are solving for the initial stress as you describe. The total deformation is the deformation at the end of load step 2. It's not zero because you have produced some "non-recoverable" plastic strain in load step 1.
You are navigating away from the AIS Discovery experience